ODE
\[ y(x) f\left (\frac {y'(x)}{y(x)},x\right )=0 \] ODE Classification
[_separable]
Book solution method
Homogeneous ODE, equation of form \(y f(x , \frac {y'}{y})\)
Mathematica ✓
cpu = 0.289583 (sec), leaf count = 28
\[\left \{\{y(x)\to 0\},\left \{y(x)\to c_1 e^{\int _1^x \text {InverseFunction}[f,1,2][0,K[1]] \, dK[1]}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) -{\it \_C1}\,{{\rm e}^{\int \!{\it RootOf} \left ( f \left ( {\it \_Z},x \right ) \right ) \,{\rm d}x}}=0,y \left ( x \right ) =0 \right \} \] Mathematica raw input
DSolve[f[y'[x]/y[x], x]*y[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 0}, {y[x] -> E^Integrate[InverseFunction[f, 1, 2][0, K[1]], {K[1], 1, x}]*C[1]}}
Maple raw input
dsolve(y(x)*f(diff(y(x),x)/y(x),x) = 0, y(x),'implicit')
Maple raw output
y(x) = 0, y(x)-_C1*exp(Int(RootOf(f(_Z,x)),x)) = 0